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Recent problems solved by 'stanbon'

stanbon answered: 57288 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299, >>Next

Mixture_Word_Problems/393541: a spice mixture is 25% thyme.How many grams of thyme must be added to a 12 g. of mixture to increase the thyme content to 40%? 1 solutions Answer 279273 by stanbon(57361)   on 2011-01-11 21:45:35 (Show Source): You can put this solution on YOUR website! a spice mixture is 25% thyme.How many grams of thyme must be added to a 12 g. of mixture to increase the thyme content to 40%? --------------- Equation: thyme + thyme = thyme 0.25x + 1.0(12-x) = 0.40*12 --- Multiply thru by 100 to get: 25x + 100*12-100x = 40*12 -75x = -60*12 x = 9.6 g (amt of 25% mixture needed in the final mix) 12-x = 2.4 g (amt of pure thyme needed in the final mix) =============== Cheers, Stan H.

Permutations/393533: 3 cards are chosen at random from a standard 52-card deck. What is the probability that they form a pair? (A 3-card hand is a pair if two of the cards match in rand but the third card is different.) 1 solutions Answer 279271 by stanbon(57361)   on 2011-01-11 21:39:10 (Show Source): You can put this solution on YOUR website! 3 cards are chosen at random from a standard 52-card deck. What is the probability that they form a pair? (A 3-card hand is a pair if two of the cards match in rand but the third card is different.) --- Pick a type of card: 13 ways Pick a pair of that type: 4C2 = 6 ways ---- Pick a 3rd card that is not that type: 48 ways ---- P(event as described) = [13*6*48]/52C3 = 3744/22100 = 0.1694 ================= Cheers, Stan H.

Permutations/393530: Suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. What is the probability that (a) they all come up heads? (b) the penny and nickel both come up heads? (c) the penny and dime both come up the same? (d) at least 15 cents wort of coins come up heads? 1 solutions Answer 279270 by stanbon(57361)   on 2011-01-11 21:33:57 (Show Source): You can put this solution on YOUR website! Suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. What is the probability that (a) they all come up heads?:::: (1/2)^4 = 1/16 -------------------------------------- (b) the penny and nickel both come up heads? (1/2)(1/2)*1*1 = 1/4 --------------------------------------- (c) the penny and dime both come up the same? 2*(1/4)(1/4)*1*1 = 1/8 --------------------------------------- (d) at least 15 cents worth of coins come up heads? I'll leave that to you. Take a look at the 16 points in the sample space and see how many combinations of coins has value 15 cents or greater. ----------------------- Cheers, Stan H.

Money_Word_Problems/393524: Computer A can do a job in 4 hours. Computer B can do the same job in 2 hours. How long will it take them to complete the job working together? 1 solutions Answer 279267 by stanbon(57361)   on 2011-01-11 21:28:48 (Show Source): You can put this solution on YOUR website! Computer A can do a job in 4 hours. Computer B can do the same job in 2 hours. How long will it take them to complete the job working together? ------------- A rate = 1/4 job/hr B rate = 1/2 job/hr --- Together rate: 1/x job/hr ----------------------------- Equation: rate + rate = together rate 1/4 + 1/2 = 1/x --- Multiply thru by 4x to get: x + 2x = 4 3x = 4 x = 4/3 = 1hr and 20 min (time to do the job together) ==================== Cheers, Stan H. ===============

Average/393529: State is 0.1 is written in scientific notation. If not, write it in scientific notation. 1 solutions Answer 279265 by stanbon(57361)   on 2011-01-11 21:25:44 (Show Source): You can put this solution on YOUR website! State if 0.1 is written in scientific notation. No If not, write it in scientific notation. 1.0x10^-1 ============ Cheers, Stan H.

Matrices-and-determiminant/393527: 2a-3b=-8 4a+3b=-34 I am supposed to be using either substitution, elimination, or inverse matrices to solve. Thanks in advance for your time and help! 1 solutions Answer 279264 by stanbon(57361)   on 2011-01-11 21:23:41 (Show Source): You can put this solution on YOUR website! 2a-3b=-8 4a+3b=-34 ----------- Add to eliminate the b-terms: --- 6a = -42 --- a = -7 --- Solve for "b": 2a-3b=-8 2(-7)-3b = -8 -14-3b = -8 Add 14 to both sides to get: -3b = 6 b = -2 ============== cheers, Stan H.

Percentage-and-ratio-word-problems/393477: Hello i have a geometry promblem: The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is 450 cm. 1 solutions Answer 279244 by stanbon(57361)   on 2011-01-11 20:20:11 (Show Source): You can put this solution on YOUR website! Hello i have a geometry promblem: The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is 450 cm. -------------- 3:5:7 is the same as 3x:5x:7x --- Equation: 3x+5x+7x = 450 15x = 450 x = 30 --- 3x = 90 5x = 150 7x = 210 ============= Cheers, Stan H.

decimal-numbers/393478: Please help me solve this problem: What decimal is equal to 2/5? Please show work. My step son is just starting... Thanks!! 1 solutions Answer 279242 by stanbon(57361)   on 2011-01-11 20:18:15 (Show Source): You can put this solution on YOUR website! What decimal is equal to 2/5? --- You have to show your step son how to divide a larger number into a smaller number. --- 5)2 --- = 5)2.000 --- = 0.4 ================== Cheers, Stan H.

Age_Word_Problems/393476: What is Henry’s age when told that he is 5 times as old as his son, but will in 4 years time be only 3 times as old? 1 solutions Answer 279241 by stanbon(57361)   on 2011-01-11 20:15:45 (Show Source): You can put this solution on YOUR website! What is Henry’s age when told that he is 5 times as old as his son, but will in 4 years time be only 3 times as old? --------------------- Equations: h = 5s h+4 = 3(s+4) --- Substitute for "h" and solve for "s": 5s+4 = 3s+12 2s = 8 s = 4 (Son's age now) --- Solve for "h": h = 5s h = 5*4 = 20 (Henry's age now) ============================= Cheers, Stan H. ===========

Travel_Word_Problems/393475: Car One leaves on time and travels at 50 mph. Car Two leaves one hour later and travels at 75 mph. For how long does each car travel before the second car catches up to the first? 1 solutions Answer 279239 by stanbon(57361)   on 2011-01-11 20:12:10 (Show Source): You can put this solution on YOUR website! Car One leaves on time and travels at 50 mph. Car Two leaves one hour later and travels at 75 mph. For how long does each car travel before the second car catches up to the first? -------------- First car DATA: rate = 50 mph ; time = x hrs ; distance = rt = 50x miles -------------------------------- Second car DATA: rate = 75 mph ; time = x-1 hrs ; distance = rt = 75(x-1) miles -------------- Equation: distance = distance 50x = 75(x-1) 50x = 75x-75 -25x = -75 x = 3 hrs (1st car time) --- x-1 = 2 hrs (2nd car time) ============================== cheers, Stan H.

Polynomials-and-rational-expressions/393473: factor 3x^2+14x+15 1 solutions Answer 279237 by stanbon(57361)   on 2011-01-11 20:08:21 (Show Source): You can put this solution on YOUR website! factor 3x^2+14x+15 --- 3x^2+5x+9x+15 --- x(3x+5)+3(3x+5) --- (3x+5)(x+3) =============== Cheers, Stan H.

Distributive-associative-commutative-properties/393472: How do you foil 2x^2+x-3 1 solutions Answer 279236 by stanbon(57361)   on 2011-01-11 20:05:39 (Show Source): You can put this solution on YOUR website! How do you foil 2x^2+x-3 ---------- 2x^2+3x-2x-3 --- x(2x+3)-(2x+3) --- (2x+3)(x-1) =============== This is called inverse FOIL. Cheers, Stan H.

Expressions-with-variables/393433: two cars leave town at the same time going in opposite directions. one car travels 44mi/h and the other travels 55mi/h. in how many hours will they be 297 miles apart? 1 solutions Answer 279220 by stanbon(57361)   on 2011-01-11 19:32:22 (Show Source): You can put this solution on YOUR website! two cars leave town at the same time going in opposite directions. one car travels 44mi/h and the other travels 55mi/h. in how many hours will they be 297 miles apart? --- They are separating at the rate of 44+55 = 99 mph --- time = distance/rate tim = 297/99 = 3 hrs ================================ Cheers, Stan H.

test/393436: Negative times positive equals? 1 solutions Answer 279217 by stanbon(57361)   on 2011-01-11 19:28:23 (Show Source): You can put this solution on YOUR website! Negative

Exponents-negative-and-fractional/393432: I need help solving the below problem 4{3[5(y − 3) + 9] + 2(y + 8)} 1 solutions Answer 279216 by stanbon(57361)   on 2011-01-11 19:27:47 (Show Source): You can put this solution on YOUR website! 4{3[5(y − 3) + 9] + 2(y + 8)} --- Working from the inside to the outside: 4{3[5(y − 3) + 9] + 2(y + 8)} --- = 4{3{5y-15)+9] + 2y+16} --- = 4{15y-45+9]+ 2y+16} --- = 4{17y-20} --- = 68y-80 ============== Cheers, Stan H.

Linear-systems/393431: how do i write an equation of a line when i am given the point and the slope? 1 solutions Answer 279213 by stanbon(57361)   on 2011-01-11 19:22:24 (Show Source): You can put this solution on YOUR website! how do i write an equation of a line when i am given the point and the slope? --- One way to do it. -- If the point is (a,b) and the slope is m the equation is: y-b = m(x-a) ==================== Cheers, Stan H.

Equations/393417: Hi umm my question is write mathemetical symbols into algebric symbols A number minus seven i wrote f-7 is that correct two reduced by a number-I wrote- 2-g double a number and add three- 2n+3 divider a number by seven then add six-5'(21-y) Translate into english phrases 19-(3n)-three times a number subtract nineteen 12n+7- Twelve times a number plus seven 8 x (n+4)- A number plus four times eight writer algebric equation for each statement one half the number of students is 21- 1.5x=21 write an algebric equiation for each sentence a) the perimeter of a square is 156cm square has s on one side.- 156/4=39 39*4 1 solutions Answer 279203 by stanbon(57361)   on 2011-01-11 19:04:14 (Show Source): You can put this solution on YOUR website! write mathemetical symbols into algebraic symbols: ------------------- A number minus seven i wrote f-7 is that correct::OK ---- two reduced by a number-I wrote- 2-g:: OK ---------------------- double a number and add three- 2n+3:OK ----------------- divide a number by seven then add six::(n/7)+6 --------------------------------- Translate into english phrases 19-(3n)::: The difference between nineteen and three times a number. -------------------------------- 12n+7- The sum of twelve times a number and seven. ----------------------- 8 x (n+4)- The product of eight and the sum of a number and four. --------------------- write algebric equation for each statement: one half the number of students is 21- (1/2)x=21 ----- write an algebric equiation for each sentence a) the perimeter of a square is 156cm ; the square has s on one side 4s = 156 cm ---------------- Cheers, Stan H.

Age_Word_Problems/393416: leila is x years old.old is she six years ago in algebraic expressions? 1 solutions Answer 279200 by stanbon(57361)   on 2011-01-11 18:54:45 (Show Source): You can put this solution on YOUR website! leila is x years old.old is she six years ago in algebraic expressions? ----- Ans: x-6 yrs. old ==================== Cheers, Stan H.

Finance/393387: loan= $500,000 part A = 6% each year part B = 11% each year if the bank recieves $43,750 in interest each year, how much was loaned at 6%? 1 solutions Answer 279193 by stanbon(57361)   on 2011-01-11 18:25:04 (Show Source): You can put this solution on YOUR website! loan= $500,000 part A = 6% each year part B = 11% each year if the bank recieves $43,750 in interest each year, how much was loaned at 6%? ------------------------ Equations: Quantity Eq::: x + y = 500,000 --- Interest Eq::0.11x + 0.06y = 43,750 ==================== Multiply thru the 1st by 11. Multiply thru the 2nd by 100. -------------------------------- 11x + 11y = 11*500,000 11x + 6y = 4375000 ----------------------------- Subtract the 2nd from the 1st and solve for "y": 5y = 1,125,000 --- y = $225,000 (amt. invested at 6%) ================= 500,000- 225,000 = 275,000 (amt. invested at 11% =============================================== Cheers, Stan H. =============

Percentage-and-ratio-word-problems/393368: A $150.00 coat was marked down $30.00. What percent was it marked down? 1 solutions Answer 279179 by stanbon(57361)   on 2011-01-11 17:55:44 (Show Source): You can put this solution on YOUR website! A $150.00 coat was marked down $30.00. What percent was it marked down? ---- Amount of mark down = 30 dollars --- Percent of mark down is 30/150 = 1/5 = 20% --------------- Cheers, Stan H. =============

Equations/393364: I'm trying to help a friend. I'm 50 yrs old and can't remember how to do this. What type of equation is this? And can you solve it? 16-(4m+9)=-5m-5+m+12 I know you have to do the same thing on each side of the equation. 1 solutions Answer 279177 by stanbon(57361)   on 2011-01-11 17:53:41 (Show Source): You can put this solution on YOUR website! 16-(4m+9)=-5m-5+m+12 --- 16-4m-9 = 5m-5+m+12 --- 7-4m = 6m+7 10m = 0 --- m = 0 ========== That's what friends are for. ========== Cheers, Stan H.

test/393355: if f(x) =x/3 +5 what is the value of f^-1 (-6) 1 solutions Answer 279175 by stanbon(57361)   on 2011-01-11 17:49:40 (Show Source): You can put this solution on YOUR website! if f(x) =x/3 +5 what is the value of f^-1 (-6) ---- Let y = -6 and solve for "x": -6 = (x/3)+5 x/3 = -11 x = -33 ------------------------------ f^-1(-6) = -33 ================== Cheers, Stan H. =============

Rational-functions/393361: Arthur can edit 15 essays in 10 h. Debra needs 15 h to do the same job. If they work together, how long will it take them to edit the essays? 1 solutions Answer 279172 by stanbon(57361)   on 2011-01-11 17:41:41 (Show Source): You can put this solution on YOUR website! Arthur can edit 15 essays in 10 h. Debra needs 15 h to do the same job. If they work together, how long will it take them to edit the essays? ----------------- Arthur DATA: time = 10 hr/job ; rate = 1/10 job/hr ------- Debra DATA: time = 15 hr/job ; rate = 1/15 job/hr -------- Together DATA: time = x hr/job ; rate = 1/x job/hr ================== Equation: rate + rate = together rate 1/10 + 1/15 = 1/x --- Multiply thru by 30x to get: 3x + 2x = 30 5x = 30 x = 6 hrs (amt. of time needed for them to do the job together) ======================== Cheers, Stan H. ===============

Linear_Algebra/393359: find the standard form of the equation of the line that passes through the points (9,-3) and (-1,-7) 1 solutions Answer 279171 by stanbon(57361)   on 2011-01-11 17:36:27 (Show Source): You can put this solution on YOUR website! find the standard form of the equation of the line that passes through the points (9,-3) and (-1,-7) ----------------- slope = (-7--3)/(-1-9) = -4/-10 = 2/5 ------------------ Form: y = mx+b You have y = -3 when x=9 and m = 2/5 ---------------------- -3 = (2/5)(9)+b --- b = -3-(2/5)9 b = -6.6 ------- Equation: y = (2/5)x - (33/5) --- To get the standard form, multiply thru by 5 to get: 5y = 2x - 33 -2x+5y = -33 ==================== Cheers, Stan H. ============== ===========

test/393356: (3x^1.25) -4=1 , what is x? 1 solutions Answer 279170 by stanbon(57361)   on 2011-01-11 17:31:38 (Show Source): You can put this solution on YOUR website! (3x^1.25) -4=1 , what is x? --- 3x^1.25 = 5 --- x^1.25 = 5/3 --- x^(5/4) = 5/3 --- [x^(5/4)]^(4/5) = (5/3)^(4/5) ---- x = 1.5048 ================ Cheers, Stan H. ================

Mixture_Word_Problems/393357: A goldsmith has two alloys of gold, the first being 70% pure and the second being 60% pure. How many ounces of the 60% pure gold must be used to make 100 ounces of an alloy which will be 66% gold? 1 solutions Answer 279169 by stanbon(57361)   on 2011-01-11 17:26:54 (Show Source): You can put this solution on YOUR website! A goldsmith has two alloys of gold, the first being 70% pure and the second being 60% pure. How many ounces of the 60% pure gold must be used to make 100 ounces of an alloy which will be 66% gold? ------------ Equation: gold + gold = gold 0.70x + 0.60(100-x) = 0.66*100 --- Multiply thru by 100 to get: 70x + 60*100 - 60x = 66*100 10x = 6*100 x = 60 oz (amt. of 70% alloy needed in the mix) --- 100-x = 40 oz (amt of 60% alloy needed in the mix) ============== Cheers, Stan H.

Graphs/393353: write the slope-intercept form of the equation of the line passing through the points (-6,-2) and parallel to this line y=-3x-4 1 solutions Answer 279168 by stanbon(57361)   on 2011-01-11 17:19:17 (Show Source): You can put this solution on YOUR website! write the slope-intercept form of the equation of the line passing through the points (-6,-2) and parallel to this line y=-3x-4 ----------------------------- The given line has a slope of -3. ---- Any line parallel to it must have a slope of -3. ---- Equation Form: y = mx + b --- You know x = -6 when y = -2 and you know m = -3 ; solve for "b": ---- -2 + -3(-6)+b b = -2-18 = -20 ---- Equation: y = -3x-20

Linear-equations/393347: PLEASE HELP! (: my teacher JUST informed us that there is a test on slope tomorrow, and we only spent two days learning about the topic! I really need help on things like finding the difference between slopes,writing equations of slopes, and how to write an equation in slope-intercept form . PLEASE HELP! 1 solutions Answer 279167 by stanbon(57361)   on 2011-01-11 17:14:17 (Show Source): You can put this solution on YOUR website! Post a couple of your problems and/or use Google to search for "algebra lines slopes" on the web. ---- Cheers, Stan H.

test/393346: 157=6x^2/5 -233 what is x? 1 solutions Answer 279166 by stanbon(57361)   on 2011-01-11 17:09:34 (Show Source): You can put this solution on YOUR website! 157=6x^2/5 -233 what is x? --- 6x^(2/5) = 390 ---- x^(2/5) = 65 --- [x^(2/5)]^(5/2) = 65^(6/5) ---- x = 149.79... Cheers, Stan H.

test/393344: If f(x) = -4x +5 and g(x) = |x-6| then what is f(g)(-2)) 1 solutions Answer 279164 by stanbon(57361)   on 2011-01-11 17:06:17 (Show Source): You can put this solution on YOUR website! If f(x) = -4x +5 and g(x) = |x-6| then what is f(g)(-2)) ------ f[g(-2)] = f[-2-6|] = f(8) = -4*8+5 = -27 ============================ Cheers, Stan H. =======

Quadratic_Equations/393329: What is the solution to the factoring problem 2x^2-24x^3+14x^2? I tried it this way: 2x^2(x^-12x+7), but was not able to simplify beyond this point. Thanks 1 solutions Answer 279163 by stanbon(57361)   on 2011-01-11 17:02:10 (Show Source): You can put this solution on YOUR website! What is the solution to the factoring problem 2x^2-24x^3+14x^2? ---- It is not an equation, so it does not have a "solution". ------------- 2x^2-24x^3+14x^2 Simplify: -24x^3+16x^2 It can be factored: -8x^2(3x-2) ============ Cheers, Stan H.